Math Problem Statement

25x 2 −81

Solution

To solve the expression 25x28125x^2 - 81, you can factor it using the difference of squares method.

Step 1: Recognize the difference of squares.

The expression is of the form a2b2a^2 - b^2, where:

  • a=5xa = 5x (since (5x)2=25x2(5x)^2 = 25x^2)
  • b=9b = 9 (since 92=819^2 = 81)

Step 2: Apply the difference of squares formula.

The difference of squares formula is:

a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b)

Step 3: Substitute the values of aa and bb into the formula.

25x281=(5x9)(5x+9)25x^2 - 81 = (5x - 9)(5x + 9)

So, the expression 25x28125x^2 - 81 factors to:

(5x9)(5x+9)(5x - 9)(5x + 9)

Would you like more details or have any questions?


Here are five related questions:

  1. How do you solve a quadratic equation like (5x9)(5x+9)=0(5x - 9)(5x + 9) = 0?
  2. Can you explain how to factor expressions that are not perfect squares?
  3. What are some real-life applications of the difference of squares formula?
  4. How would you expand (5x9)(5x+9)(5x - 9)(5x + 9) back to the original expression?
  5. How does factoring help in solving polynomial equations?

Tip: Remember, recognizing patterns like the difference of squares can simplify the process of factoring complex expressions!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Difference of Squares

Formulas

Difference of squares formula: a^2 - b^2 = (a - b)(a + b)

Theorems

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Suitable Grade Level

Grades 9-12